Question

8. Suppose that the demand curve for wheat is Q=120-10p and the supply curve is Q= 10p. The government imposes a price ceiling of p S4 per unit. a. How do the equilibrium price and quantity change? (round quantities to the nearest integer and round prices to the nearest penny) 60 The equilibrium quantity without the price ceiling is ceiling is $ and the price without the price The equilibrium quantity with the price ceiling is b. What effect does this ceiling have on consumer surplus, producer surplus, and deadweight loss? The change in consumer surplus (CS) is S The change in producer surplus (PS) is S The deadweight loss (DWL) is S (round your answer to the nearest penny). (round your answer to the nearest penny). (round your answer to the nearest penny).

Answer 1

1. At equilibrium, Quantity demanded = Quantity supplied

Without Price ceiling,

120 - 10p = 10p

20p = 120

P = 120/20

P=6

Substitute p = 6 in Quantity supplied

Qs = 10p

Q=10*6

Q = 60

Without price ceiling: Equilibrium Price = $6, Equilibrium Quantity = 60

At equilibrium, Quantity demanded = Quantity supplied

With Price ceiling, p = $4

Substitute p = $4

Qs = 10p

Qs = 10*4

Q = 40

With price ceiling: Equilibrium Quantity = 40

2. Demand curve: Q = 120-10P

When Q = 0, P = $12

Supply curve: Q = 10P

When Q = 0, P = 0

Consumer surplus = (1/2)*b*h = (1/2)*(12-6)*60

Consumer surplus = $180

Producer surplus = (1/2)*(6-0)*60

Producer surplus = $180

Total surplus = Consumer surplus + Producer surplus = 180 + 180

Total surplus = $360

Due to price ceiling:

New price = $4 and Quantity = 40

Consumer surplus = [(1/2) * (12-8) * 40] + [(4*40)]

(Area of triangle + area of square)

Consumer surplus = $240

Producer surplus = (1/2)*(4-0)*40

Producer surplus = $80

Change in consumer surplus = 240 – 180

Change in consumer surplus = $60

Change in producer surplus = 80 – 180

Change in producer surplus = -$100

New total surplus = 240+80 = $320

Deadweight loss = Total surplus – New total surplus

Deadweight loss = 360 – 320

Deadweight loss = $40